MULTIVARIATE FORECASTING WITH RECURRENT NEURAL NETWORKS¶
FILENAME: Analysis Notebook.ipynb
PROJECT: Multivariate Financial Forecasting
DATE CREATED:24-APR-20
DATE UPDATED:24-APR-20
TASK: Develop and implement a recurrent neural network
PURPOSE: Given a multivariate dataset, forecast and predict the corresponding response value for each record
INTENT: The purpose of this project is to conduct exploratory analysis of the provided data set and apply both supervised and unsupervised algorithms in order to extract meaniningful information in support for future open source analysis. The project is broken down into two separate projects, with each project having four (4) distinct phases:
PROJECT: Randomized Budget Data
Environment Setup
Data ETL
Data Exploration
Model Development
Create randomm arrays to store the test values:
YEAR +5: yr5_forecast
YEAR +4: yr4_forecast
YEAR +3: yr3_forecast
YEAR +2: yr2_forecast
YEAR +1: yr1_forecast
YEAR +0: plan
YEAR -1: approp
YEAR -2: obligate
PROJECT APPLICATION: BUDGET ANALYSIS¶
In [61]:
from IPython.display import Image
from IPython.core.display import HTML
Image(filename = "data/rnn.png", width=750, height=750)
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PHASE 1: PROJECT SETUP¶
Import the required ML & neural net libraries
In [5]:
from scipy import stats
import tensorflow as tf
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import MinMaxScaler
from tensorflow import keras
from tensorflow.keras import layers
from sklearn.model_selection import train_test_split
from sklearn.pipeline import Pipeline
from tensorflow.python.keras.models import Sequential
from tensorflow.python.keras.layers import Dense
from tensorflow.python.keras.wrappers.scikit_learn import KerasRegressor
In [8]:
def init_array(df_length):
'''
DESCRIPTION: A function to create and return a two_dimensional array with randomized float values
'''
length = df_length
yr5_forecast= np.random.randint(low = 100000, high = 30000000, size = df_length)
yr4_random = np.random.uniform(low=0.5, high=1.5, size=df_length)
yr4_forecast = np.round(yr5_prep * yr4_random,2)
yr3_random = np.random.uniform(low=0.6, high=1.4, size=df_length)
yr3_forecast = np.round(yr4_forecast * yr3_random,2)
yr2_random = np.random.uniform(low=0.7, high=1.3, size=df_length)
yr2_forecast = np.round(yr3_plan * yr2_random,2)
yr1_random = np.random.uniform(low=0.8, high=1.2, size=df_length)
yr1_forecast = np.round(yr2_approp * yr1_random,2)
plan_random = np.random.uniform(low=0.6, high=1.3, size=df_length)
plan_val = np.round(yr1_oblig * plan_random,2)
approp_random = np.random.uniform(low=0.6, high=1.2, size=df_length)
approp_val = np.round(plan_val * approp_random,2)
oblig_random = np.random.uniform(low=0.7, high=1.0, size=df_length)
oblig_val = np.round(approp_val * oblig_random,2)
raw_df = pd.DataFrame(columns=['yr5_prep','yr4_forecast','yr3_plan','yr2_approp','yr1_oblig','yr0_exe'])
raw_df['yr5_forecast'] = yr5_forecast
raw_df['yr4_forecast'] = yr4_forecast
raw_df['yr3_forecast'] = yr3_forecast
raw_df['yr2_forecast'] = yr2_forecast
raw_df['yr1_forecast'] = yr1_forecast
raw_df['planned'] = plan_val
raw_df['appropriated'] = approp_val
raw_df['obligated'] = oblig_val
return raw_df
PHASE 2: DATA ETL¶
Create random arrays to store the test values:
- YEAR +5: yr5_forecast
- YEAR +4: yr4_forecast
- YEAR +3: yr3_forecast
- YEAR +2: yr2_forecast
- YEAR +1: yr1_forecast
- YEAR +0: plan
- YEAR -1: approp
- YEAR -2: obligate
Create the training array
In [9]:
train_df = init_array(10000)
train_df.tail(10)
Out[9]:
In [10]:
col_list = list(train_df.columns)
col_list
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PHASE 3: DATA EXPLORATION¶
In [11]:
dataset = train_df.copy()
dataset.tail(10)
Out[11]:
In [12]:
import plotly.graph_objects as go
import numpy as np
np.random.seed(1)
y5 = dataset.yr5_prep
y4 = dataset.yr4_forecast
y3 = dataset.yr3_plan
y2 = dataset.yr2_approp
y1 = dataset.yr1_oblig
y0 = dataset.yr0_exe
fig = go.Figure()
fig.add_trace(go.Box(x=y0, name = "yr5_prep"))
fig.add_trace(go.Box(x=y1, name = "yr4_forecast"))
fig.add_trace(go.Box(x=y2, name = "yr3_plan"))
fig.add_trace(go.Box(x=y3, name = "yr2_approp"))
fig.add_trace(go.Box(x=y4, name = "yr1_oblig"))
fig.add_trace(go.Box(x=y5, name = "yr0_exe"))
fig.show()
In [13]:
budget_pair = train_df[['yr5_prep','yr4_forecast','yr3_plan','yr2_approp','yr1_oblig','yr0_exe']]
sns.set(style="ticks", color_codes=True)
sns.pairplot(budget_pair)
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PHASE 4: MODEL DEVELOPMENT¶
Convert dataframe to numpy arrays
In [14]:
x=dataset.iloc[:, 0:5].to_numpy()
y=dataset.iloc[:,5].to_numpy()
x
Out[14]:
In [15]:
y=np.reshape(y, (-1,1))
y
Out[15]:
Scale the data from 0 -> 1
In [16]:
scaler_x = MinMaxScaler()
scaler_y = MinMaxScaler()
print(scaler_x.fit(x))
xscale=scaler_x.transform(x)
print(scaler_y.fit(y))
yscale=scaler_y.transform(y)
Segregate master data to 'train', 'test', 'split'
In [17]:
X_train, X_test, y_train, y_test = train_test_split(xscale, yscale)
Verify the array shape
In [18]:
X_train.shape
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y_train is the response variable
In [19]:
y_train.shape
Out[19]:
Build the recurrent neural network (RNN)¶
In [20]:
model = Sequential()
model.add(Dense(10, input_dim=5, kernel_initializer='normal', activation='relu'))
model.add(Dense(5, activation='relu'))
model.add(Dense(1, activation='linear'))
model.summary()
In [21]:
model.compile(loss='mse', optimizer='adam', metrics=['mse','mae'])
Fit the RNN model to our data¶
In [22]:
history = model.fit(X_train, y_train, epochs=150, batch_size=50, verbose=1, validation_split=0.2)
Plot the Loss Test¶
In [23]:
fig = go.Figure()
fig.add_trace(go.Scatter(y=history.history['loss'],
mode='lines',
name='Train'))
fig.add_trace(go.Scatter(y=history.history['val_loss'],
mode='lines+markers',
name='Validation'))
fig.update_layout(
autosize=False,
width=1500,
height=750,
title = "Train vs. Validation Loss Test",
xaxis=dict(
title_text="No. of epochs",
titlefont=dict(size=20),
),
yaxis=dict(
title_text="Loss Value",
titlefont=dict(size=20),
)
)
fig.show()
Predict Values¶
Create a new array with dummy data and test the model's effeftiveness against it
In [24]:
predict_full = init_array(25000)
valid_df = predict_full.iloc[:,:-1]
valid_df.tail(100)
Out[24]:
Convert the dataframe to a two dimensional numpy array
In [25]:
valid_array = valid_df.to_numpy()
valid_array
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Validate the shape of the newly created array
In [26]:
valid_array.shape
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Predict all response values for each of the 25,000 records¶
In [27]:
predict_val = model.predict(valid_array)
predict_val
Out[27]:
Merge the numpy predictor array as a standalone column to the predict_full dataframe
In [28]:
predict_full['predict_values'] = predict_val
predict_full.tail(10)
Out[28]:
Calculate the difference in actual ('yr0_exe') and predicted ('predict_values') model values and assign a difference value for each record in the 'delta' column
In [29]:
predict_full['delta'] = (predict_full['yr0_exe'] - predict_full['predict_values']) / predict_full['yr0_exe']
predict_full.tail(10)
Out[29]:
Display the histogram of the delta values (i.e distribution)
In [30]:
fig = px.histogram(predict_full, x="delta",marginal="rug", # can be `box`, `violin`
hover_data=predict_full.columns, color_discrete_sequence=['indianred'], opacity = 0.5)
fig.update_layout(
autosize=True,
title = "Actual vs Prediction value Historgram ")
fig.show()
Display distribution of box & whisker plot for response and predict values
In [38]:
yr5 = dataset.yr0_exe
yr6 = predict_full.predict_values
fig = go.Figure()
fig.add_trace(go.Box(x=yr5, name = "yr0_exe"))
fig.add_trace(go.Box(x=yr6, name = "predict_values"))
fig.show()
Plot the model evaluation¶
Retrieve the statistical parameters for the linear model
In [32]:
x = predict_full['yr0_exe']
y = predict_full['predict_values']
slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)
print(" Slope: {}\n Intercept: {}\n R-squared: {}\n P-Value: {}\n Standard Error: {}". format(slope, intercept, r_value, p_value, std_err))
Plot the response values (original) against the predicted values
In [33]:
fig = px.scatter(predict_full, x="yr0_exe", y="predict_values", trendline="ols", opacity=0.25, color_discrete_sequence=['green'])
fig.update_layout(
autosize=False,
width=1000,
height=750,
title = "Response values vs predicted values scatterplot",
xaxis=dict(
title_text="yr0_exe values (Response Values)",
titlefont=dict(size=20),
),
yaxis=dict(
title_text="predict_values (Predicted Values)",
titlefont=dict(size=20),
)
)
fig.show()
GEOPLOT¶
In [40]:
df_size = len(predict_full)
df_size
Out[40]:
In [49]:
lat_random = np.random.uniform(low=19.50139, high=64.85694, size=df_size)
long_random = np.random.uniform(low=-161.75583, high=-68.01197, size=df_size)
In [50]:
len(long_random)
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In [51]:
geo_df = predict_full.copy()
geo_df['latitude'] = lat_random
geo_df['longitude'] = long_random
geo_df.tail(10)
Out[51]:
In [56]:
fig = px.scatter(geo_df[:50], x="longitude", y="latitude", opacity=0.25, size = "predict_values", color_discrete_sequence=['green'])
fig.update_layout(
autosize=False,
width=1000,
height=750,
title = "US Map of Budget points",
xaxis=dict(
title_text="Longitude",
titlefont=dict(size=20),
),
yaxis=dict(
title_text="Latitude",
titlefont=dict(size=20),
)
)
fig.show()
In [58]:
from urllib.request import urlopen
import json
with urlopen('https://raw.githubusercontent.com/plotly/datasets/master/geojson-counties-fips.json') as response:
counties = json.load(response)
In [ ]:
PROGRAM END¶
In [34]:
program_end = t.time() - program_start
elapsed = round(program_end, 2)
print("Total time for program execution is {} seconds".format(elapsed))
In [59]:
import descartes
import geopandas gpd
Out[59]:
In [ ]: